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arXiv 1108.0348cond-mat.mes-hallcond-mat.str-el
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电子-声子耦合对石墨烯朗道能级的影响

Effects of electron-phonon coupling on Landau levels in graphene

Adam Pound, J. P. Carbotte, E. J. Nicol

摘要:

我们计算了在外加磁场中电子与声子耦合的石墨烯的态密度。我们发现,耦合到一个爱因斯坦模式的频率$ω_E$不仅移动和加宽的朗道能级(LLS),但从根本上改变了DOS通过引入一组新的峰值在能量$E_n\pmω_E$,其中$E_n$是能量的$n$ th LL。如果这些新峰中的一个足够接近LL,则它导致LL分裂成两个;如果系统包含能隙,则LL可以分裂成三个。新的峰值出现在间隔$(-ω_E,ω_E)$之外,使得该间隔中的LL基本上不受影响。如果化学势大于声子频率,则第零个LL位于间隔之外,并且可以分裂,消除其与单个狄拉克点的关联。我们发现,耦合到一个扩展的声子分布,如洛伦兹或德拜光谱不定性地改变这些结果。

英文摘要:

We calculate the density of states (DOS) in graphene for electrons coupled to a phonon in an external magnetic field. We find that coupling to an Einstein mode of frequency $ω_E$ not only shifts and broadens the Landau levels (LLs), but radically alters the DOS by introducing a new set of peaks at energies $E_n\pmω_E$, where $E_n$ is the energy of the $n$th LL. If one of these new peaks lies sufficiently close to a LL, it causes the LL to split in two; if the system contains an energy gap, a LL may be split in three. The new peaks occur outside the interval $(-ω_E,ω_E)$, leaving the LLs in that interval largely unaffected. If the chemical potential is greater than the phonon frequency, the zeroth LL lies outside the interval and can be split, eliminating its association with a single Dirac point. We find that coupling to an extended phonon distribution such as a Lorentzian or Debye spectrum does not qualitatively alter these results.

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